Reaching nirvana with a defaultable asset?

We study the optimal dynamic portfolio exposure to predictable default risk to explain the search for yield by means of defaultable assets observed before the 2007-2008 crisis and in its aftermath. Under no arbitrage, default risk is compensated by an yield pickup that can strongly attract aggressive investors via an investment-horizon e¤ect in their optimal non-myopic portfolios. We show it by extending the optimal dynamic nirvana-type portfolio problem of Kim and Omberg (1996) to a defaultable risky asset and by rigorously proving their longstanding nirvana-solution conjecture. We achieve such a contribution to the portfolio optimization literature by means of a careful, closed-form-yielding adaptation to our defaultable-asset setting of the general convex duality approach of Kramkov and Schachermayer (1999, 2003).